Clean up frontend editing actions
The frontend editing actions in t3lib_frontendedit have some small inconsistencies and duplicated code that can be cleaned up.
Calling editing actions based directly on the frontend editing cmd (ie. edit -> $this->edit()) can cause problems with reserved keywords. While this isn't a problem in the current code, the frontend editing controller is extensible so an additional controller that needs to handle the 'new' cmd would have problems. This is fixed by prepending the cmd with 'do' instead (ie. edit -> $this->doEdit()).
Additionally, inconsistencies with saving and duplicated code in the various move functions have been addressed.
(issue imported from #M10372)